用量子门作为无Church不可判定性和Godel不完全性的通用算术算法的物理模型
A Quantum Gate as a Physical Model of an Universal Arithmetical Algorithm without Church's Undecidability and Godel's Incompleteness
摘要：
在这项工作中，我们定义了一个通用的算术算法，通过标准的量子力学形式主义，称为通用的qm算术算法。用通用的qm算术算法可以判定（实现、计算）任何可判定的算术公式（运算）。由称为qm算术一对一的通用qm算术算法定义的算术对应于通常算术的可判定部分。我们证明了在qm-算术中不可判定的算术公式（运算）不存在（不能一致定义）。或者，我们证明了qm-算术没有不可判定的部分。这样，我们表明，qm算术，既不持有教会的不可判定性，也不持有哥德尔的不完全性，是可判定的和完整的。最后，提出了用qm算法解决算法基础问题的建议。
英文摘要：
In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formulas (operations) cannot exist (cannot be consistently defined). Or, we prove that qm-arithmetic has no undecidable parts. In this way we show that qm-arithmetic, that holds neither Church's undecidability nor Godel's incompleteness, is decidable and complete. Finally, we suggest that problems of the foundation of the arithmetic, can be solved by qm-arithmetic.
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